Prof Santiago Hernandez from the University of La Coruña, Spain presented a lecture on “The Road to Aeroelastic Design of Optimisation of Long Span Suspension Bridges” as part of a series of lectures on the topic of Structural Optimisation given at the Wessex Institute of Technology.
This type of bridge, Prof Hernandez explained, requires accurate analysis of the structures due to wind loads. He referred in particular to the following aspects:
I Wind related Failures of Suspension Bridges
150 years ago there was a renowned failure of a chain suspension bridge in Brighton in the UK. Another important failure was the one in the Menay Strait in Wales, built by Thomas Telford. The Wheeling Bridge in USA, also in the XIX Century was destroyed by the wind. The most famous of all was the Tacoma Narrows Bridge which had an 800m, designed by well known engineers in spite of which it started to experience substantial displacement even under mild wind conditions. It failed in 1940 with wind speeds of 67km/hour wind when it underwent a series of vibration modes. It was not clear then why the bridge failed as it was designed for winds of more than 150km/hour. The problem was the lack of understanding of the wind force effects. The Tacoma Bridge disaster was a major starting point for wind aeroelasticity effects. There are two main methodologies for designing these bridges, shown below.
II Experimental aided design of Suspension Bridges
A reduced model of the bridge is built and tried in a wind tunnel. It consists of a boundary layer wind testing. The experiment aims to find the wind velocity leading to instabilities by increasing the wind flow in the laboratory until increasingly large displacements appears in the model. This type of testing provides a good representation of the bridge behaviour but is very expensive and not wholly accurate, due to experimental error.
III Hybrid Approach for the Aeroelastic Design of Suspension Bridges
In this case, a section of the bridge, such as part of the deck is tested in the wind tunnel to determine the behaviour of that section. It identifies the forces created by the wind and the behaviour of the section. This leads to the identification of the flutter derivatives.
Those coefficients are used in the finite element computational model of the bridge, which is used to identify the aeroelastic modes of vibration in the structure. Flutter is computed by finding the eigenvalue solutions having zero damping coefficient.
IV Long Span Bridge Projects / Sensitivity Analysis
There are many long span suspension bridges to be built around the world. The current methodology can be used in this regard as well as to study Sensitivity Analysis of Flutter Speed when varying the inertia modules. By varying these modules one can find different sensitivity equations to produce an optimal solution.
These analyses are computationally demanding because they require:
- Computer evaluation of natural eigenmodes.
- Computer evaluation of aeroelastic eigenvalues.
- Computer evaluation of sensitivity analysis
Prof Hernandez showed results for the flutter speed of the Great Belt Bridge in Denmark. He demonstrated the need to consider more modes in the analysis and not just the first few. The results can be dramatically different when considering for instance 17 modes, resulting in difference for flutter wind speed from 90km/hour for one mode to 62.5km/hour in the case of 17 modes. The values of the sensitivity derivatives also vary greatly.
He then explained the analysis carried out by his group for the design of the projected Messina Bridge. There was considerable argument regarding the flutter speed for the bridge, which is an important problem due to the major costs involved. They found that the flutter speed for the structure varies from 97m/s to 87m/s, both higher than the design wind speed.